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Title: Topological structures in Colombeau algebras: topological ℂ̃-modules and duality theory
Authors: Garetto, Claudia
Keywords: Algebras of generalized functions
Duality theory
Modules over the ring of complex generalized numbers
Issue Date: 2005
Publisher: © Springer
Citation: GARETTO, C., 2005. Topological structures in Colombeau algebras: topological ℂ̃-modules and duality theory. Acta Applicandae Mathematicae, 88 (1), pp. 81 - 123
Abstract: We study modules over the ring ℂ̃ of complex generalized numbers from a topological point of view, introducing the notions of ℂ̃-linear topology and locally convex ℂ̃-linear topology. In this context particular attention is given to completeness, continuity of ℂ̃-linear maps and elements of duality theory for topological ℂ̃-modules. As main examples we consider various Colombeau algebras of generalized functions. © Springer 2005.
Description: This article was published in the journal, Acta Applicandae Mathematicae [© Springer]. The final publication is available at Springer via http://dx.doi.org/10.1007/s10440-005-6700-y
Version: Accepted for publication
DOI: 10.1007/s10440-005-6700-y
URI: https://dspace.lboro.ac.uk/2134/17311
Publisher Link: http://dx.doi.org/10.1007/s10440-005-6700-y
ISSN: 0167-8019
Appears in Collections:Published Articles (Maths)

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